# Two Pulleys with two acceleration and two tensions (Diagram included)

• Wara
In summary: Can you tell me what happened to T2?In summary, the problem involves two masses connected by strings and a pulley. The upper block slides along the table with a coefficient of friction of 0.32. Using equations (1)-(4), we can calculate the tensions (T1 and T2) and accelerations (a1 and a2) of the system. By eliminating T1 and substituting for T2 and a2, we can solve for the magnitude of T1 and a1.
Wara
pulley

## Homework Statement

Two masses are attached together by means of light inextensible strings and light frictionless pulleys as shown in the diagram. The system is released and the upper block slides along the table. The coefficient of friction between this block and the table is 0.32. Calculate the magnitude of the tensions (T1 and T2) and accelerations while the blocks are acceleration.
http://content.screencast.com/users/Waraa/folders/Snagit/media/bc6a12fc-dd79-4db6-91a4-1057f75aca6e/03.10.2012-15.11.45.png

## Homework Equations

(1) m1a1 = T1 - μmg
(2) m2aa = m2g - T2
(3) 2T1 = T2
(4) 2a2 = a1

## The Attempt at a Solution

T1 = 113.7N
T2 = 196N

(1) + (2) + (3) + (4)
m1a1 + m2aa + 2T1 + 2a2 = T1 - μmg + m2g - T2 + T2 + a1
2a2 = T1 - μmg + m2g + a1

I'm stuck right there. Am I even doing it right?

Last edited by a moderator:
Wara said:

## Homework Statement

Two masses are attached together by means of light inextensible strings and light frictionless pulleys as shown in the diagram. The system is released and the upper block slides along the table. The coefficient of friction between this block and the table is 0.32. Calculate the magnitude of the tensions (T1 and T2) and accelerations while the blocks are acceleration.
http://content.screencast.com/users/Waraa/folders/Snagit/media/bc6a12fc-dd79-4db6-91a4-1057f75aca6e/03.10.2012-15.11.45.png

## Homework Equations

(1) m1a1 = T1 - μmg
(2) m2aa = m2g - T2
(3) 2T1 = T2
(4) 2a2 = a1

## The Attempt at a Solution

T1 = 113.7N
T2 = 196N

(1) + (2) + (3) + (4)
m1a1 + m2aa + 2T1 + 2a2 = T1 - μmg + m2g - T2 + T2 + a1
2a2 = T1 - μmg + m2g + a1

I'm stuck right there. Am I even doing it right?
Hi Wara!
Wara said:
(1) m1a1 = T1 - μmg
(2) m2aa = m2g - T2
(3) 2T1 = T2
(4) 2a2 = a1

Fine so far!

ok, now you should substitute for a2 and T2 from (3) and (4) into (2):

(1) m1a1 = T1 - μmg
(2) m2a1/2 = m2g - 2T1

then eliminate T1

Last edited by a moderator:
tiny-tim said:
Hi Wara!

Fine so far!

ok, now you should substitute for a2 and T2 from (3) and (4) into (2):

(1) m1a1 = T1 - μmg
(2) m2a1/2 = m2g - 2T1

then eliminate T1

Thank you so much.

## What is the purpose of using two pulleys in a system?

The use of two pulleys allows for a change in the direction of the applied force, which can be useful in various applications such as lifting heavy objects or transmitting power.

## How does the acceleration of the pulleys affect the system?

The acceleration of the pulleys can affect the overall acceleration of the system. In this diagram, the two pulleys have the same acceleration, which results in a balanced system. However, if one pulley were to have a greater acceleration, it would cause a difference in the tensions and could potentially result in an unbalanced system.

## What are the factors that affect the tensions in a system with two pulleys?

The tensions in a system with two pulleys are affected by the masses of the objects being lifted, the accelerations of the pulleys, and the friction in the system. The angle of the ropes and the coefficient of friction between the pulleys and the ropes can also play a role in determining the tensions.

## Can the tensions in a system with two pulleys ever be equal?

Yes, the tensions in a system with two pulleys can be equal if the masses of the objects being lifted are equal and the accelerations of the pulleys are also equal. In this case, the system would be balanced and the two tensions would cancel each other out.

## What is the relationship between the tensions and the accelerations in this system?

The tensions and accelerations in this system have an inverse relationship. As the accelerations of the pulleys increase, the tensions in the ropes decrease. This is due to the conservation of energy and the distribution of forces in a system with two pulleys.

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